The probability threshold method has been widely adopted to assess collision risks for space objects. The general method for collision probability can reduce the problem to a two-dimensional integral over a circular region in a plane normal to the relative velocity vector. It provides sufficiently accurate results, but does not reveal the direct connection between collision probability and conjunction geometry.

    For our space missions and spacecrafts, dangerous objects in low-earth-orbit are to our most concern. Through our analysis using Two-line Element Sets, more than 90% space objects are in near circular orbits with eccentricities less than 0.1, and most encounters are happening between two space objects in near-circular orbit.. Based on such a prerequisite, we develop a different method which gives an explicit expression to compute collision probability which is expressed as an function of the radical and the cross section components of the relative position and error covariance. The expression is compact and advantageous to analyze the influencing factors of the collision probability directly.

    A computer program is developed to implement the technique, and the calculation results are compared with the general method. It shows that this method is applicable to most collision risk assessments in near-circular orbit.

By with XU Xiaoli

Fig.2. Variation of collision probability versus the relative position error.

The work by X.L. Xu, Y.Q. Xiong has been published in Research in Astronomy and Astrophysics. Please see the link for more details: http://www.raa-journal.org/raa/index.php/raa/article/view/1587